What's different besides a different story and a different set of enemies in different locations? Not much.
Of course, just with those few differences, you've already got an almost entirely different game. IIRC, one of the main side-effects of that choice is that you're choosing between a "missile-based" ally and a "close combat" ally.
I think the most important difference is the set of enemies you're up against, because that determines what skills your pilots are going to pick up. One story leads very quickly to the powerful "Pilot DMG" skills which then allows you to capture complete wanzers by taking out the pilot without totally destroying wanzer parts.